Kalkylator för bestämda och oegentliga integraler

Kalkylatorn försöker beräkna bestämda integraler (dvs. med integrationsgränser), inklusive oegentliga, och visar stegen.

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Solution

Your input: calculate $$$\int_{0}^{1}\left( \sqrt{x} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\sqrt{x} d x}=\frac{2 x^{\frac{3}{2}}}{3}$$$ (for steps, see indefinite integral calculator)

According to the Fundamental Theorem of Calculus, $$$\int_a^b F(x) dx=f(b)-f(a)$$$, so just evaluate the integral at the endpoints, and that's the answer.

$$$\left(\frac{2 x^{\frac{3}{2}}}{3}\right)|_{\left(x=1\right)}=\frac{2}{3}$$$

$$$\left(\frac{2 x^{\frac{3}{2}}}{3}\right)|_{\left(x=0\right)}=0$$$

$$$\int_{0}^{1}\left( \sqrt{x} \right)dx=\left(\frac{2 x^{\frac{3}{2}}}{3}\right)|_{\left(x=1\right)}-\left(\frac{2 x^{\frac{3}{2}}}{3}\right)|_{\left(x=0\right)}=\frac{2}{3}$$$

Answer: $$$\int_{0}^{1}\left( \sqrt{x} \right)dx=\frac{2}{3}\approx 0.666666666666667$$$

Kalkylator för bestämda och oegentliga integraler

Beräkna bestämda och oegentliga integraler steg för steg

Solution